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`find_minloc(`

`data` [, `sign`, diagonal=`diagonal`,
/degree, /subgrid, /coords])

By default, seeks local minima in `data`

and returns their
positions as indices to `data`

. If `/coords`

is specified,
then the coordinates of the positions are returned (with the first
dimension sampling the different coordinates). `data`

must be
numerical and may have multiple dimensions.

If

is specified, then it must be an array with one
element per dimension of `diagonal`

. The elements that are equal
to 0 indicate which dimensions are not checked for a local minimum. The
elements that are equal to 1 and 2 (after conversion to type
`data``long`

) indicate in which dimensions checking is performed. The
elements that are equal to 2 indicate in which dimensions checked
directions may be diagonal. All such directions either have non-zero
coordinate offsets only in those dimensions, or have only a single
non-zero coordinate offset (i.e., a non-diagnonal or orthogonal
direction). Only approved directions are checked for their data
curvature. If

contains `diagonal``n1`

ones and
`n2`

twos, then the number of directions per data element in
`n`

dimensions that will be considered is equal to ```
m = (3^n2
- 1)/2 + n1
```

.

For example, regard a two-dimensional array. We’ll call the first
dimension the east-west direction and the second one the north-south
dimension. Then, if

, all points are
returned that are local minima in the east-west direction without
regards to any other direction. If `diagonal` = [1,0]

, then
all points are returned that are local minima in the east-west direction
and also in the north-south direction, without regards to the other
(northeast-southwest, southeast-northwest) directions. If
`diagonal` = [1,1]

, then all directions are checked.
`diagonal` = [2,2]

For a three-dimensional array, if

, then
the only checked directions that have a non-zero third coordinate offset
are those that are along the 3rd axis. If `diagonal` = [2,2,0]

, then only directions along the first two axes are checked.
`diagonal` =
[1,1,0]

If `/degree`

is specified, then the number of directions per data
element where the data shows a local minimum is returned instead. This
number always lies between 0 and the total number `m`

of directions
given above. `find_min(`

returns an array
with 1s at all positions returned by `data`, /degree) eq m`find_min(`

, but
the latter form is considerably faster because for each element it stops
checking as soon as a direction without a local minimum is found. For
noise data in arbitrary numbers of dimensions, on average at most 2
local minimum comparisons per data element are performed if
`data`)`/degree`

is not specified, compared to `m`

, which is grows
exponentially with the number of dimensions in the worst case, if
`/degree`

is specified..

The used algorithm decides whether a particular data point is a local minimum by looking at its nearest neighbors only. This means that it cannot decide if a region in which all adjacent data values are equal constitutes a local minimum. Such regions are ignored.

See also: local_min, find_min, find_minloc

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